# How do you factor x^3-x^2-10x-8?

Apr 5, 2016

$f \left(x\right) = \left(x + 1\right) \left(x + 2\right) \left(x - 4\right)$

#### Explanation:

f(x) = x^3 - x^2 - 10x - 8.
We find out that
f(-1) = -1 -1 + 10 - 8 = 0,
then, one factor is (x + 1).
After division -->
$f \left(x\right) = \left(x + 1\right) \left({x}^{2} - 2 x - 8\right)$
The trinomial in parentheses can be factored.
Find 2 numbers knowing sum (-2) and product (-8).
They are (2) and (-4)
$\left({x}^{2} - 2 x - 8\right) = \left(x + 2\right) \left(x - 4\right)$
$f \left(x\right) = \left(x + 1\right) \left(x + 2\right) \left(x - 4\right)$